REVISITING CLASSICAL GRAIN BOUNDARY DIFFUSION MODELS

D. Gryaznov,
J. Fleig (Vienna University of Technology, Vienna, Austria),
J. Maier (MPI for Solid State Research, Stuttgart, Germany).

Prediction of transport properties of nanomaterials is of great interest. This work was performed in collaboration with the Max Planck Institute for Solid State Research in the framework of PhD study of D. Gryaznov completed on 20 September 2006 by a successful defense of PhD Thesis at Stuttgart University. The main scope of present study was to analyze limitations of classical grain boundary diffusion models (Fisher's model, Whipple's solution, Le Claire' relation) used to find the grain boundary diffusivity from measured diffusion profiles. Recently, such modern experimental techniques as secondary ion mass spectroscopy (SIMS) in the depth-profiling mode were improved to give new possibilities for researchers. Namely, SIMS allows one to measure very shallow diffusion profiles. Nevertheless, the classical grain boundary diffusion models are based on different approximations, supposing sufficiently high temperatures and/or long diffusion times. However, nanocrystalline materials impose the new conditions, i.e. short diffusion times and low temperatures. Consequently, Le Claire's relation was validated for the new conditions on the basis of numerical integrations of the exact Whipple solution. Also, the classical grain boundary diffusion models treat a grain boundary being perpendicular to the free surface. The finite element method was used to integrate Fisher's model and to take into account different grain boundaries orientations with respect to diffusion direction, which is particularly relevant for studying diffusion in nanocrystalline materials. Additionally, ionic materials are characterized by space charge layer adjacent to grain boundary core. This property is completely ignored in the classical grain diffusion models despite the fact that it can significantly alter the transport properties of ionic materials.
On the basis of integrations mentioned above, a procedure was established, which allows us to find properly the grain boundary diffusivity. This procedure can be easy used since it requires the grain diffusion length only. Moreover, new analytical dependences were observed for a maximum of the diffusion profile derivative and its positional coordinate as functions of the diffusion time and ratio of the grain and grain boundary diffusivities. The procedure gives accurate values of grain boundary diffusivity for bi- and polycrystals at short and long diffusion times if orientations of the grain boundaries can be ignored. It was also estimated that the latter effect underestimates the grain boundary diffusivity by using the standard Le Claire relation. The analytical dependence for the maximum of the diffusion profile derivative not only gives an alternative procedure for deducing the grain boundary diffusivity but also sufficiently improves determination of the grain boundary diffusivity in ionic materials.


UNIVERSAL DESCRIPTION OF ELECTRONIC CORRELATIONS IN DOUBLE QUANTUM DOTS

V. Kashcheyevs,
A. Aharony and O. Entin-Wohlman (Ben Gurion University of the Negev, Ber Sheeva, Israel),
A. Schiller (Hebrew University of Jerusalem, Israel).

Quantum dots are very important for the optoelectronic applications. In collaboration with Ben Gurion University of the Negev, Ber Sheeva, and Hebrew University of Jerusalem, we have put forward a theoretical framework for accurate characterization of strongly correlated states in double quantum dots. Such systems consist of two nanoscale objects with discrete electronic states that are coupled to two leads. In strong magnetic fields only one non-degenerate electronic state dominates the transport in each of the two dots. Strong Coulomb repulsion between the dots can force the two-level system into the regime of a single occupancy, where it effectively becomes a charge qubit. The superposition of the charge states (being in the first or in the second dot) is strongly affected by tunneling of the itinerant electrons from the leads, which play the role of a coherent fermionic environment. Recent theoretical and experimental studies have identified a number of intriguing phenomena in this system such as level population inversion and oscillations, transmission phase lapses and sharp transmission resonances.
Our work presented a unified quantitative explanation for these phenomena in terms of coherent dynamics of the pseudo-spin, and identifies the relevant physical mechanism, namely competition between the polarizing effect of the effective magnetic field and the Kondo-screening by the coherent environment. By a proper rotation of the quantum-mechanical representation for the charge states on the dots and in the leads, we maped the system exactly onto a generalize Anderson impurity model. This mapping alone allowed for a novel Friedel sum rule based exact expression for the low temperature conductance through degenerate levels. For the most general case of interest we developed a quantitative pseudo-spin description (Kondo type Hamiltonian), which reveals renormalization of the effective magnetic field and anisotropy of the exchange couplings. Exploiting the exact Bethe ansatz solution of the Kondo model, we have put forward very accurate expressions for the occupation numbers and the linear conductance. Our analytical results are in a very good agreement with advanced numerical renormalization group calculations, and call for an experimental test.


EXPERIMENTAL AND THEORETICAL STUDIES OF NANOSTRUCTURED MATERIALS

A. Popov and Yu. Zhukovskii,
C. Balasubramanian, S. Bellucci, M. Cestelli Guidi, A. Grilli, M. Piccinini, and A. Raco, (National Laboratory of Frascati, Italy),
V. Baranov, V. Biryukov, Yu. Chesnokov, and V. Maisheev (Institute for High Energy Physics, Protvino, Russia),
I. Bolesta, S. Velgosh, and I. Karbovnyk (National University of Lviv, Ukraine).

In collaboration with Laboratori Nazionali di Frascati (LNF) at Synchrotron Radiation Facility using both XANES (X-ray absorption near edge spectroscopy) and FTIR (Fourier transform infrared spectroscopy) techniques, we have studied different AlN nanosystems using spectroscopic methods, in order to investigate both tribological and electronic properties of nanostructured materials. III group nitrides nanostructures attract enhanced attention of both experimentalists and theorists, due to numerous technological applications, mainly in nano- and optoelectronics. Comparison has been performed between measurements by standard X-ray diffraction (XRD) and X-ray absorption spectroscopy (XAS) at the K-edge of Al, which is sensitive to the local order and correlated to the local and empty density of states of wide band-gap semiconductor. Preliminary XAS simulations were also performed. Correlations between XRD and XAS have been drawn. Moreover, a comparison has been performed by infrared (IR) absorption both in the mid- and in the far-IR ranges between different AlN samples: powders, nanoparticles and nanotubes. Our results clearly show changes connected with the electronic properties and the optical phonon modes of AlN nano-systems.

In collaboration with LNF, Frascati, we have analyzed the effect of N vacancies (neutral F centers), which could be created by a soft irradiation of nanotubes (NT), on both the electronic and structural properties of AlN single-walled (SW) NTs. For this aim, we have considered 1D periodic models of armchair- and zigzag-type chirality and performed their DFT calculations using the CRYSTAL-03 code. To simulate structural reconstruction around each point defect of AlN NTs, we have optimized their geometry. To achieve the limit of single vacancy for both nanotube chiralities, we have considered three sets of inter-defect distances repeated along the axes of these nanotubes. The Mulliken charges on the F centers are found to be -2 e, close to the effective charges on N ions. However, the electron charge density re-distributions around the F center are substantial for both chiralities. They remain well localized along NT axis and disturb the electron density on the nearest atoms across NTs. N vacancies results induce one-electron energy levels in the NTs band gaps with main contributions from 3p and 3s atomic orbitals of the nearest Al atoms. The larger is the inter-defect distance on AlN SW NTs, the smaller dispersion of defect levels.

In collaboration with National University of Lviv and LNF, Frascati, we have also studied an influence of (Cdi)n metallic clusters on the optical absorption and phonon spectra of CgI2 crystals, in order to understand the role of Cd nano- and microcluster in context of CgI2 crystal application as possible scintillator material and very promising materials for second harmonic generation. Metallic clusters of spherical shape were formed during the growth of non-stoichiometric crystals. Radii of clusters fall in the range from 10 to 500 nm, according to scanning electron microscopy (SEM) data. The density of clusters was estimated from fractal dimension calculations. In the framework of Mie theory, the spectral and size dependencies on extinction coefficients have been calculated. From the experimentally obtained spectra it is evident that metallic clusters are responsible for the bands in the transparency region of CdI2 crystals (360-430 nm) and peaks in mid-infrared absorption spectra, which are not present in those of the pure cadmium iodide. The nature of this additional optical and infrared absorption is concerned with bulk and surface plasmons and surface phonon modes of metallic clusters, respectively. Transmittance in the far-IR (50 to 600 cm-1) and mid-IR (600 to 1300 cm-1) regions was measured at the infrared station of the Synchrotron Radiation facility of LNF. The activation of crystals by diffusion during/after growth does not have any significant effect on their far IR spectra. Relative intensity of IR peaks varies depending on the impurity. This result is in a good agreement with SEM analysis and optical data.

Recently invented technique of crystal bending has been applied to produce samples with a high curvature. In collaboration with LNF, Frascati, and Institute for High Energy Physics, Protvino, we have investigated the deflection of a positron beam with energies of 400-700 MeV, available in the beam test facility (BTF) of LNF, by means of bent silicon crystals. In recent years this technique was successfully applied for crystal undulator production. We have observed positron bending by a crystal lattice, presumably being guided by a channeling phenomenon, deflecting the beam by about 10 milliradian over a 1 mm length of silicon. This technique may result in the use of the channeling effect for steering particle beams at energies below 1 GeV for the purpose of producing beams of low emittance with enhanced stability for medical and biological applications. By giving to nanotubes a controlled bending of a few milliradian, we could deflect the channeled particles out of the incident beam. Carbon nanotubes (CNT) proposed for particle channelling have been synthesized at LNF and then have been characterized there by SEM, TEM and AFM to obtain ratio and dimensions of the CNTs. SEM images show that the ratio of NTs is very high (more than 70%). Single-wall-CNTs have an average diameter 1.3 nm and a length of several microns.

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